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Difficulty:
45%
(medium)
Question Stats:
69% (02:21) correct
31%
(02:37)
wrong
based on 511
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Point K = (A,0), Point G = (2A + 4, \(\sqrt{2A+ 9}\)). Is the distance between point K and G prime?
(1) A^2 – 5A – 6 = 0
(2) A > 2
(1) A^2 – 5A – 6 = 0
(2) A > 2
10 Jan 2013, 16:51
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Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the distance between point K and G prime?
The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).
Hence, the distance between points G and K is \(d=\sqrt{(2A+4-A)^2+(\sqrt{2A+9}-0)^2}=\sqrt{(A+5)^2}=|A+5|\)
(1) A^2 – 5A – 6 = 0 --> \((A-6)(A+1)=0\) --> \(A=6\) or \(A=-1\) --> \(d=|A+5|=11=prime\) or \(d=|A+5|=4\neq{prime}\). Not sufficient.
(2) A > 2. If \(A=3\), then \(d=|A+5|=8\neq{prime}\) but if \(A=6\), then \(d=|A+5|=11=prime\). Not sufficient.
(1)+(2) Since from (2) A > 2, then from (1) \(A=6\), thus \(d=|A+5|=11=prime\). Sufficient.
Answer: C.
Hope it's clear.
The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).
Hence, the distance between points G and K is \(d=\sqrt{(2A+4-A)^2+(\sqrt{2A+9}-0)^2}=\sqrt{(A+5)^2}=|A+5|\)
(1) A^2 – 5A – 6 = 0 --> \((A-6)(A+1)=0\) --> \(A=6\) or \(A=-1\) --> \(d=|A+5|=11=prime\) or \(d=|A+5|=4\neq{prime}\). Not sufficient.
(2) A > 2. If \(A=3\), then \(d=|A+5|=8\neq{prime}\) but if \(A=6\), then \(d=|A+5|=11=prime\). Not sufficient.
(1)+(2) Since from (2) A > 2, then from (1) \(A=6\), thus \(d=|A+5|=11=prime\). Sufficient.
Answer: C.
Hope it's clear.
General Discussion
BillyZ
Current Student
Joined: 14 Nov 2016
Last visit: 24 Jan 2026
Posts: 1,135
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
Posts: 1,135
30 Mar 2017, 22:52
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